Quark anomalous magnetic moment in an extreme magnetic background from perturbative QCD

We compute the one-loop QCD correction to the photon-quark-antiquark vertex in an extremely strong magnetic background, i.e., one in which <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msqrt><a:mrow><a:mi>e</a:mi><a:mi>B</a:mi></a:mrow></a:msqrt></a:math> is much larger than all other mass scales. We resort to the lowest-Landau level approximation, and consider on-shell fermions. We find that the total magnetic moment is such that the anomalous magnetic moment contributes to the electric part <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mo>∼</c:mo><c:mi>i</c:mi><c:msub><c:mi>E</c:mi><c:mn>3</c:mn></c:msub><c:msub><c:mi>σ</c:mi><c:mn>3</c:mn></c:msub></c:math>, the other contributions to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi mathvariant="bold-italic">B</e:mi><e:mo>·</e:mo><e:mi mathvariant="bold-italic">σ</e:mi></e:mrow></e:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>i</i:mi><i:mi mathvariant="bold-italic">E</i:mi><i:mo>·</i:mo><i:msub><i:mrow><i:mi mathvariant="bold-italic">σ</i:mi></i:mrow><i:mrow><i:mo>⊥</i:mo></i:mrow></i:msub></i:mrow></i:math> being completely suppressed. We show results for the anomalous magnetic moment of quarks up and down, scaled by their values in the vacuum, as a function of the external magnetic field, considering dressed gluons and a renormalization scale <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msub><m:mrow><m:mi>μ</m:mi></m:mrow><m:mrow><m:mover accent="true"><m:mrow><m:mi>MS</m:mi></m:mrow><m:mrow><m:mo stretchy="true">¯</m:mo></m:mrow></m:mover></m:mrow></m:msub><m:mo>=</m:mo><m:msqrt><m:mrow><m:mo stretchy="false">|</m:mo><m:mi>e</m:mi><m:mi>B</m:mi><m:mo stretchy="false">|</m:mo></m:mrow></m:msqrt></m:mrow></m:math>. Published by the American Physical Society 2024